Anna buys a house in $2008$ for $$250,000,$ with a $6\%30$y mortgage.

After making $16$ years worth of payments $($total of $192),$ she does a "cash out refi" and refinances into a new $30$y loan, at $5\%.$ Her payments are the same as they were on the $2008$ loan. How much cash did she take out? $($Answer is between $$100$K and $$125$K$)$